In which type of design is sphericity particularly relevant?

In which type of design is sphericity particularly relevant?

• A. Repeated measures design with within-subject factors
• B. Between-subjects design
• C. Cross-sectional design
• D. One-way ANOVA with independent groups

Answer: (A)

Sphericity matters when you have a repeated measures design, where the same participants are measured under multiple conditions or time points. In this setup, the within-subject factor creates related measurements, and sphericity refers to the equality of variances of the differences between all pairs of levels of that within-subject factor. This assumption keeps the F-tests in repeated measures ANOVA accurate. It becomes especially important when the within-subject factor has more than two levels, because with three or more levels the relationships among the repeated measures are more complex, and violations can inflate the Type I error rate. If sphericity is violated, corrections like Greenhouse-Geisser or Huynh-Feldt are applied to adjust the degrees of freedom and keep the test valid. Other designs—where you compare independent groups or where measurements are cross-sectional—do not rely on sphericity. Between-subjects designs or one-way ANOVA with independent groups assume equal variances across groups but not the covariance structure among repeated measures, so sphericity is not the focal concern there.

Sphericity matters when you have a repeated measures design, where the same participants are measured under multiple conditions or time points. In this setup, the within-subject factor creates related measurements, and sphericity refers to the equality of variances of the differences between all pairs of levels of that within-subject factor. This assumption keeps the F-tests in repeated measures ANOVA accurate. It becomes especially important when the within-subject factor has more than two levels, because with three or more levels the relationships among the repeated measures are more complex, and violations can inflate the Type I error rate. If sphericity is violated, corrections like Greenhouse-Geisser or Huynh-Feldt are applied to adjust the degrees of freedom and keep the test valid.

Other designs—where you compare independent groups or where measurements are cross-sectional—do not rely on sphericity. Between-subjects designs or one-way ANOVA with independent groups assume equal variances across groups but not the covariance structure among repeated measures, so sphericity is not the focal concern there.